Conformational analysis of protein and nucleic acid fragments with the new grid search algorithm FOUND

The new computer algorithm FOUND, which is implemented as an integrated module of the DYANA structure calculation program, is capable of performing systematic local conformation analyses by exhaustive grid searches for arbitrary contiguous fragments of proteins and nucleic acids. It uses torsion angles as the only degrees of freedom to identify all conformations that fulfill the steric and NMR-derived conformational restraints within a contiguous molecular fragment, as defined either by limits on the maximal restraint violations or by the fragment-based DYANA target function value. Sets of mutually dependent torsion angles, for example in ribose rings, are treated as a single degree of freedom. The results of the local conformation analysis include allowed torsion angle ranges and stereospecific assignments for diastereotopic substituents, which are then included in the input of a subsequent structure calculation. FOUND can be used for grid searches comprising up to 13 torsion angles, such as the backbone of a complete -helical turn or dinucleotide fragments in nucleic acids, and yields a significantly higher number of stereospecific assignments than the precursor grid search algorithm HABAS.     

Determination of the conformation of d(GGAAATTTCC)2 in solution by use of 1H NMR and restrained molecular dynamics

The conformation of the putative bent DNA d(GGAAATTTCC)2 in solution was studied by use of 1H NMR and restrained molecular dynamics. Most of the resonances were assigned sequentially. A total of 182 interproton distance restraints were determined from two-dimensional nuclear Overhauser effect spectra with short mixing times. Torsion angle restraints for each sugar moiety were determined by qualitative analysis of a two-dimensional correlated spectrum. Restrained molecular dynamics was carried out with the interproton distances and torsion angles incorporated into the total energy function of the system in the form of effective potential terms. As initial conformations for restrained molecular dynamics, classical A-DNA and B-DNA were adopted. The root mean square deviation (rmsd) between these two conformations is 5.5 A. The conformations obtained by use of restrained molecular dynamics are very similar to each other, the rmsd being 0.8 A. On the other hand, the conformations obtained by use of molecular dynamics without experimental restraints or restrained energy minimization depended heavily on the initial conformations, and convergence to a similar conformation was not attained. The conformation obtained by use of restrained molecular dynamics exhibits a few remarkable features. The second G residue takes on the BII conformation [Fratini, A. V., Kopka, M. L., Drew, H. R., & Dickerson, R. E. (1982) J. Biol. Chem. 257, 14686-14707] rather than the standard BI conformation. There is discontinuity of the sugar puckering between the eighth T and ninth C. The minor groove of the oligo(dA) tract is rather compressed. As a result, d(GGAAATTTCC)2 is bent.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

A restraint molecular dynamics and simulated annealing approach for protein homology modeling utilizing mean angles

Background

We have developed the program PERMOL for semi-automated homology modeling of proteins. It is based on restrained molecular dynamics using a simulated annealing protocol in torsion angle space. As main restraints defining the optimal local geometry of the structure weighted mean dihedral angles and their standard deviations are used which are calculated with an algorithm described earlier by Döker et al. (1999, BBRC, 257, 348–350). The overall long-range contacts are established via a small number of distance restraints between atoms involved in hydrogen bonds and backbone atoms of conserved residues. Employing the restraints generated by PERMOL three-dimensional structures are obtained using standard molecular dynamics programs such as DYANA or CNS.

Results

To test this modeling approach it has been used for predicting the structure of the histidine-containing phosphocarrier protein HPr from E. coli and the structure of the human peroxisome proliferator activated receptor γ (Ppar γ). The divergence between the modeled HPr and the previously determined X-ray structure was comparable to the divergence between the X-ray structure and the published NMR structure. The modeled structure of Ppar γ was also very close to the previously solved X-ray structure with an RMSD of 0.262 nm for the backbone atoms.

Conclusion

In summary, we present a new method for homology modeling capable of producing high-quality structure models. An advantage of the method is that it can be used in combination with incomplete NMR data to obtain reasonable structure models in accordance with the experimental data.

     

Homology modeling by the ICM method

Five models have been built by the ICM method for the Comparative Modeling section of the Meeting on the Critical Assessment of Techniques for Protein Structure Prediction. The targets have homologous proteins with known three-dimensional structure with sequence identity ranging from 25 to 77%. After alignment of the target sequence with the related three-dimensional structure, the modeling procedure consists of two subproblems: side-chain prediction and loop prediction. The ICM method approaches these problems with the following steps: (1) a starting model is created based on the homologous structure with the conserved portion fixed and the noncon-served portion having standard covalent geometry and free torsion angles; (2) the Biased Probability Monte Carlo (BPMC) procedure is applied to search the subspaces of either all the nonconservative side-chain torsion angles or torsion angles in a loop backbone and surrounding side chains. A special algorithm was designed to generate low-energy loop deformations. The BPMC procedure globally optimizes the energy function consisting of ECEPP/3 and solvation energy terms. Comparison of the predictions with the NMR or crystallographic solutions reveals a high proportion of correctly predicted side chains. The loops were not correctly predicted because imprinted distortions of the backbone increased the energy of the near-native conformation and thus made the solution unrecognizable. Interestingly, the energy terms were found to be reliable and the sampling of conformational space sufficient. The implications of this finding for the strategies of future comparative modeling are discussed. © 1995 Wiley-Liss, Inc.     

Simultaneous single-structure and bundle representation of protein NMR structures in torsion angle space

A method is introduced to represent an ensemble of conformers of a protein by a single structure in torsion angle space that lies closest to the averaged Cartesian coordinates while maintaining perfect covalent geometry and on average equal steric quality and an equally good fit to the experimental (e.g. NMR) data as the individual conformers of the ensemble. The single representative ‘regmean structure’ is obtained by simulated annealing in torsion angle space with the program CYANA using as input data the experimental restraints, restraints for the atom positions relative to the average Cartesian coordinates, and restraints for the torsion angles relative to the corresponding principal cluster average values of the ensemble. The method was applied to 11 proteins for which NMR structure ensembles are available, and compared to alternative, commonly used simple approaches for selecting a single representative structure, e.g. the structure from the ensemble that best fulfills the experimental and steric restraints, or the structure from the ensemble that has the lowest RMSD value to the average Cartesian coordinates. In all cases our method found a structure in torsion angle space that is significantly closer to the mean coordinates than the alternatives while maintaining the same quality as individual conformers. The method is thus suitable to generate representative single structure representations of protein structure ensembles in torsion angle space. Since in the case of NMR structure calculations with CYANA the single structure is calculated in the same way as the individual conformers except that weak positional and torsion angle restraints are added, we propose to represent new NMR structures by a ‘regmean bundle’ consisting of the single representative structure as the first conformer and all but one original individual conformers (the original conformer with the highest target function value is discarded in order to keep the number of conformers in the bundle constant). In this way, analyses that require a single structure can be carried out in the most meaningful way using the first model, while at the same time the additional information contained in the ensemble remains available.     

Exploring the dynamic information content of a protein NMR structure: Comparison of a molecular dynamics simulation with the NMR and X‐ray structures of Escherichia coli ribonuclease HI

The multiconformer nature of solution nuclear magnetic resonance (NMR) structures of proteins results from the effects of intramolecular dynamics, spin diffusion and an uneven distribution of structural restraints throughout the molecule. A delineation of the former from the latter two contributions is attempted in this work for an ensemble of 15 NMR structures of the protein Escherichia coli ribonuclease HI (RNase HI). Exploration of the dynamic information content of the NMR ensemble is carried out through correlation with data from two crystal structures and a 1.7‐ns molecular dynamics (MD) trajectory of RNase HI in explicit solvent. Assessment of the consistency of the crystal and mean MD structures with nuclear Overhauser effect (NOE) data showed that the NMR ensemble is overall more compatible with the high‐resolution (1.48 Å) crystal structure than with either the lower‐resolution (2.05 Å) crystal structure or the MD simulation. Furthermore, the NMR ensemble is found to span more conformational space than the MD simulation for both the backbone and the sidechains of RNase HI. Nonetheless, the backbone conformational variability of both the NMR ensemble and the simulation is especially consistent with NMR relaxation measurements of two loop regions that are putative sites of substrate recognition. Plausible side‐chain dynamic information is extracted from the NMR ensemble on the basis of (i) rotamericity and syn‐pentane character of variable torsion angles, (ii) comparison of the magnitude of atomic mean‐square fluctuations (msf) with those deduced from crystallographic thermal factors, and (iii) comparison of torsion angle conformational behavior in the NMR ensemble and the simulation. Several heterogeneous torsion angles, while adopting non‐rotameric/syn‐pentane conformations in the NMR ensemble, exist in a unique conformation in the simulation and display low X‐ray thermal factors. These torsions are identified as sites whose variability is likely to be an artifact of the NMR structure determination procedure. A number of other torsions show a close correspondence between the conformations sampled in the NMR and MD ensembles, as well as significant correlations among crystallographic thermal factors and atomic msf calculated from the NMR ensemble and the simulation. These results indicate that a significant amount of dynamic information is contained in the NMR ensemble. The relevance of the present findings for the biological function of RNase HI, protein recognition studies, and previous investigations of the motional content of protein NMR structures are discussed. Proteins 1999;36:87–110. © 1999 Wiley‐Liss, Inc.     

Statistical analysis of RNA backbone

Local conformation is an important determinant of RNA catalysis and binding. The analysis of RNA conformation is particularly difficult due to the large number of degrees of freedom (torsion angles) per residue. Proteins, by comparison, have many fewer degrees of freedom per residue. In this work, we use and extend classical tools from statistics and signal processing to search for clusters in RNA conformational space. Results are reported both for scalar analysis, where each torsion angle is separately studied, and for vectorial analysis, where several angles are simultaneously clustered. Adapting techniques from vector quantization and clustering to the RNA structure, we find torsion angle clusters and RNA conformational motifs. We validate the technique using well-known conformational motifs, showing that the simultaneous study of the total torsion angle space leads to results consistent with known motifs reported in the literature and also to the finding of new ones.     

The structure of the double-stranded RNA pentamer 5'(CACAG) . 5'(CUGUG) determined by nuclear Overhauser enhancement measurements: interproton distance determination and structure refinement on the basis of X-ray coordinates

The structure in solution of the duplex RNA pentamer 5'(CACAG) . 5'(CUGUG), comprising the stem of the T psi C loop of yeast tRNAPhe, has been investigated by means of one- and two-dimensional nuclear Overhauser enhancement measurements. All non-exchangeable base and sugar proton resonances with the exception of the H5'/H5" sugar resonances are assigned in a sequential manner. From the relative intensities of the cross-peaks obtained in the pure-phase absorption two-dimensional nuclear Overhauser enhancement spectra at several mixing times, it is deduced that the RNA pentamer adopts an A-type conformation in solution. Cross-relaxation rates and interproton distances are determined from the time dependence of the nuclear Overhauser effects, principally by one-dimensional measurements. The structure of the RNA pentamer is then refined by restrained least-squares minimization on the basis of both distance and planarity restraints using fibre diffraction data as an initial model. The refined structure of the RNA pentamer is of the A type but exhibits local structural variations in glycosidic bond and backbone torsion angles as well as in propeller twist, base roll and base tilt angles.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

Structure of an elastin-mimetic polypeptide by solid-state NMR chemical shift analysis

The conformation of an elastin-mimetic recombinant protein, [(VPGVG)4(VPGKG)]39, is investigated using solid-state NMR spectroscopy. The protein is extensively labeled with 13C and 15N, and two-dimensional 13C-13C and 15N-13C correlation experiments were carried out to resolve and assign the isotropic chemical shifts of the various sites. The Pro 15N, 13Calpha, and 13Cbeta isotropic shifts, and the Gly-3 Calpha isotropic and anisotropic chemical shifts support the predominance of type-II beta-turn structure at the Pro-Gly pair but reject a type-I beta-turn. The Val-1 preceding Pro adopts mostly beta-sheet torsion angles, while the Val-4 chemical shifts are intermediate between those of helix and sheet. The protein exhibits a significant conformational distribution, shown by the broad line widths of the 15N and 13C spectra. The average chemical shifts of the solid protein are similar to the values in solution, suggesting that the low-hydration polypeptide maintains the same conformation as in solution. The ability to measure these conformational restraints by solid-state NMR opens the possibility of determining the detailed structure of this class of fibrous proteins through torsion angles and distances.     

The solution structure of a B-DNA undecamer comprising a portion of the specific target site for the cAMP receptor protein in the gal operon. Refinement on the basis of interproton distance data.

A restrained least squares refinement of the solution structure of the double-stranded DNA undecamer 5'd(AAGTGT-GACAT).5'd(ATGTCACACTT) comprising a portion of the specific target site of the cAMP receptor protein in the gal operon is presented. The structure is refined on the basis of both distance and planarity restraints, 2331 in all. The distance restraints comprise 150 interproton distances determined from pre-steady state nuclear Overhauser enhancement measurements and 2159 other interatomic distances derived from idealized geometry (i.e., distances between covalently bonded atoms, between atoms defining fixed bond angles, and between atoms defining hydrogen bonding in AT and GC base pairs). Two refinements were carried out and in both cases the final RMS difference between the experimental and calculated interproton distances was 0.2 A. The difference between the two refined structures is small (overall RMS difference of 0.23 A) and represents the error in the refined coordinates. Although the refined structures have an overall B-type conformation there are large variations in many of the local conformational parameters including backbone and glycosidic bond torsion angles, helical twist and propellor twist, base roll and base tilt angles.     

Spectral fitting for signal assignment and structural analysis of uniformly <Superscript>13</Superscript>C-labeled solid proteins by simulated annealing based on chemical shifts and spin dynamics

We describe an approach for the signal assignment and structural analysis with a suite of two-dimensional (13)C-(13)C magic-angle-spinning solid-state NMR spectra of uniformly (13)C-labeled peptides and proteins. We directly fit the calculated spectra to experimental ones by simulated annealing in restrained molecular dynamics program CNS as a function of atomic coordinates. The spectra are calculated from the conformation dependent chemical shift obtained with SHIFTX and the cross-peak intensities computed for recoupled dipolar interactions. This method was applied to a membrane-bound 14-residue peptide, mastoparan-X. The obtained C', C(alpha) and C(beta) chemical shifts agreed with those reported previously at the precisions of 0.2, 0.7 and 0.4 ppm, respectively. This spectral fitting program also provides backbone dihedral angles with a precision of about 50 degrees from the spectra even with resonance overlaps. The restraints on the angles were improved by applying protein database program TALOS to the obtained chemical shifts. The peptide structure provided by these restraints was consistent with the reported structure at the backbone RMSD of about 1 A.     

Restrained molecular dynamics of solvated duplex DNA using the particle mesh Ewald method

Restrained and unrestrained aqueous solution molecular dynamics simulations applying the particle mesh Ewald (PME) method to DNA duplex structures previously determined via in vacuo restrained molecular dynamics with NMR-derived restraints are reported. Without experimental restraints, the DNA decamer, d(CATTTGCATC)d(GATGCAAATG) and trisdecamer, d(AGCTTGCCTTGAG)d(CTCAAGGCAAGCT), structures are stable on the nanosecond time scale and adopt conformations in the B-DNA family. These free DNA simulations exhibit behavior characteristic of PME simulations previously performed on DNA sequences, including a low helical twist, frequent sugar pucker transitions, BI- BII(–) transitions and coupled crankshaft (–) motion. Refinement protocols similar to the original in vacuo restrained molecular dynamics (RMD) refinements but in aqueous solution using the Cornell et al. force field [Cornell et al. (1995) J. Am. Chem. Soc., 117, 5179–5197] and a particle mesh Ewald treatment produce structures which fit the restraints very well and are very similar to the original in vacuo NMR structure, except for a significant difference in the average helical twist. Figures of merit for the average structure found in the RMD PME decamer simulations in solution are equivalent to the original in vacuo NMR structure while the figures of merit for the free MD simulations are significantly higher. The free MD simulations with the PME method, however, lead to some sequence-dependent structural features in common with the NMR structures, unlike free MD calculations with earlier force fields and protocols. There is some suggestion that the improved handling of electrostatics by PME improves long-range structural aspects which are not well defined by the short-range nature of NMR restraints.     

Relaxation data in NMR structure determination: model calculations for the lysozyme-Gd3+ complex

The effect of including paramagnetic relaxation data as additional restraints in the determination of protein tertiary structures from NMR data has been explored by a systematic series of model calculations. The system used for testing the method was the 2.0 A resolution tetragonal crystal structure of hen egg white lysozyme (129 amino acid residues) and structures were generated using a version of the hybrid "distance geometry-dynamic simulated annealing" procedure. A limited set of 769 NOEs was used as restraints in all the calculations; the strengths of these were categorized into three classes on the basis of distances observed in the crystal structure. The values of 50 phi angles were also restrained on the basis of amide-alpha coupling constants calculated from the X-ray structure. Five sets of 12 structures were determined using differing sets of paramagnetic relaxation data as restraints additional to those involving the NOE and coupling constant data. The paramagnetic relaxation data were modeled on the basis of the distances of defined protons from the crystallographic binding site of Gd3+ in lysozyme. Analysis of the results showed that the relaxation data significantly improved the correspondence between the set of generated structures and the crystal structure, and that the more well defined the relaxation data, the more significant the improvement in the quality of the structures. The results suggest that the inclusion of paramagnetic relaxation restraints could be of significant value for the experimental determination of protein structures from NMR data.     

The influence of stereospecific assignments on the determination of three-dimensional structures of proteins by nuclear magnetic resonance spectroscopy. Application to the sea anemone protein BDS-I

The influence of the stereospecific assignments of beta-methylene protons and the classification of chi 1 torsion angles on the definition of the three-dimensional structures of proteins determined from NMR data is investigated using the sea anemone protein BDS-I (43 residues) as a model system. Two sets of structures are computed. The first set comprises 42 converged structures (denoted STEREO structures) calculated on the basis of the complete list of restraints derived from the NMR data, consisting of 489 interproton and 24 hydrogen bonding distance restraints, supplemented by 23 phi backbone and 21 chi 1 side chain torsion angle restraints. The second set comprises 31 converged structures (denoted NOSTEREO structures) calculated from a reduced data set in which those restraints arising from stereospecific assignments, and the corresponding chi 1 torsion angle restraints, are explicitly omitted. The results show that the inclusion of the stereospecific restraints leads to a significant improvement in the definition of the structure of BDS-I, both with respect to the backbone and the detailed arrangement of the side chains. Average atomic rms differences between the individual structures and the mean structures for the backbone atoms are 0.67 +/- 0.12 A and 0.93 +/- 0.16 A for the STEREO and NOSTEREO structures, respectively; the corresponding values for all atoms are 0.90 +/- 0.17 A and 1.17 +/- 0.17 A, respectively. In addition, while the overall fold remains unchanged, there is a small but significant atomic displacement between the two sets of structures.     

Direct structure refinement of high molecular weight proteins against residual dipolar couplings and carbonyl chemical shift changes upon alignment: an application to maltose binding protein

The global fold of maltose binding protein in complex with -cyclodextrin has been determined using a CNS-based torsion angle molecular dynamics protocol involving direct refinement against dipolar couplings and carbonyl chemical shift changes that occur upon alignment. The shift changes have been included as structural restraints using a new module, CANI, that has been incorporated into CNS. Force constants and timesteps have been determined that are particularly effective in structure refinement applications involving high molecular weight proteins with small to moderate numbers of NOE restraints. Solution structures of the N- and C-domains of MBP calculated with this new protocol are within 2 Å of the X-ray conformation.